Dear Donald: Explaining the Production Possibilities Curve

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Dear Donald:
Why do you always draw the production possibility curve of an economy in bow-out shape, instead of a straight line? I think you have made a mistake!
A production possibilities curve (PPC) shows the different combinations of two goods that an economy can produce with a given set of resources and technology. Suppose the economy produces food products and manufacturing equipment. The PPC below indicates that if the economy devotes all of its resources to producing food products, we would be at Point A, where the output combination is (M, F = 0, 150000), with M and F denoting the units of manufacturing equipment and pounds of food products, respectively. On the other hand, if the economy deveotes all of its resources to producing manufacturing equipment, we would be at Point D, where the output combination is (M, F = 7000, 0). In addition to these two extreme cases of producing only one good, the economy could choose to produce both goods, which could be at Point B or Point C. At any rate, the PPC traces out different combinations of manufacturing equipment and food products that the economy is capable of producing.  The PPC is downward sloping because we face scarcity in economic resources; to produce more of one good, we have to give up some of the other good.

As to the PPC being bow-out in shape, this is no mistake! The bow-out shape occurs because economic resources are not perfectly adaptable to the production of different goods and, thus, the opportunity cost of producing a good will increase as more and more resources are allocated to the production of that good. This is referred to as the law of increasing opportunity cost.
Think about this:  Let’s start at Point A on the graph where the economy produces only food products. As the economy begins to produce some manufacturing equipment, those resources that are relatively productive in the production of manufacturing equipment (and are relatively less productive in production of food products) will be the first assigned to produce manufacturing equipment.  In so doing, we minimize the amount of food products that the economy has to give up as the result. Sooner or later, however, resources that are relatively productive in producing manufacturing equipment (e.g., machinists) will become increasingly scarce. Thus, to further increase manufacturing output, resources relatively productive in the production of food products (e.g., farmers) will be summoned to work as machinists, driving up the opportunity costs of having more manufacturing equipment.
Is it really true that the bow-out PPC takes care of the law of increasing opportunity cost? Let’s move from Point A to Point B in the graph. Moving from A to B, the economy increases its manufacturing equipment by 2,000 units (from 0 to 2,000) at the expense of giving up 10,000 pounds of food products (from 150,000 to 140,000). So, within the range of Points A and B, the opportunity cost of one more unit of manufacturing equipment is 5 pounds of food products.  Now, let’s move from Point B to Point C. Moving from B to C, the economy increases its manufacturing equipment by another 2,000 units (from 2,000 to 4,000) at the expense of giving up 20,000 pounds of food products (from 140,000 to 120,000). So, within the range of Points B and C, the opportunity cost of one more unit of manufacturing equipment is 10 pounds of food products. This demonstrates that the opportunity cost of have one more unit of manufacturing equipment increases (from 5 pounds to 10 pounds of food products) as we increase the quantity of manufacturing equipment from 2,000 to 4,000 units. Indeed, the law of increasing opportunity cost is reflected in the bow-out PPC.